The short answer is that psychiatrists treat people with mental disorders using medications, while psychologists treat people using psychotherapy. This is a gross overgeneralization, of course, but I wanted to get it out there. For more detail, see below.
Psychiatrist
A psychiatrist is a medical doctor. They go to medical school and complete residency like any other physician. A psychiatrist’s specialty is mental disorders, ranging from mood disorders like depression to substance abuse disorders like alcoholism. Their job is to diagnose and treat psychiatric diseases, and they usually do so by providing prescription medications and following up on their patients’.
Your character’s first appointment with a psychiatrist will probably be a long one. The psychiatrist will go over your character’s symptoms, as well as all their medications, medical history, and family history. During this evaluation, the psychiatrist will also perform a detailed physical exam – though your character might not notice. A psychiatrist’s physical exam is close observation, watching the way your character moves, dresses, thinks, and talks. Once the exam is completed, they’ll explain your character’s diagnosis and, if the condition warrants it, prescribe medications and/or therapy. Subsequent appointments will be shorter – often as short as 15 minutes – and occur less and less frequently as your character improves. During these appointments, the psychiatrist will evaluate your character’s response to treatment. They’ll ask about side effects and efficacy of the medications and will adjust dosages or change medications as necessary.
While psychiatrists can technically perform therapy, they generally don’t, simply because they can’t bill very much for it. Instead, most psychiatrists will recommend that your character see a psychologist or therapist.
Psychologist
A psychologist is not a medical doctor, though most clinical psychologists have doctoral degrees, such as a Ph.D. in Psychology or a Doctor of Psychology (PsyD). A clinical psychologist’s job is to assess and treat mental, psychosocial, emotional, and behavioral issues. Many, though not all, provide psychotherapy. Psychotherapy comes in many forms, from Freudian psychoanalysis to cognitive behavioral therapy.
Psychologists use interviewing and psychotherapy techniques to help your character work through their mental illness and/or emotional struggles. They cannot prescribe medications, but they can give your character homework – exercises to practice or a journal to maintain. Therapy sessions usually last 30-60 minutes and are conducted regularly; weekly or even more frequently if your character is in crisis. Psychotherapy is often used in conjunction with medications.